\[\theta_{4}\left(z\middle|\tau\right)=\theta_{4}\left(0\middle|\tau\right)\prod%
_{n=1}^{\infty}\frac{\sin\left((n-\tfrac{1}{2})\pi\tau+z\right)\sin\left((n-%
\tfrac{1}{2})\pi\tau-z\right)}{{\sin}^{2}\left((n-\tfrac{1}{2})\pi\tau\right)}.\]